🚶♀Great review on random walks and diffusion on networks:
https://www.sciencedirect.com/science/article/pii/S0370157317302946
https://www.sciencedirect.com/science/article/pii/S0370157317302946
⌨ https://www.johndcook.com/blog/2017/12/12/efficiency-is-not-associative-for-matrix-multiplication/
John D. Cook | Applied Mathematics Consulting
Efficiency is not associative for matrix multiplication
For matrices A, B, and C, (AB)C = A(BC). The two sides of the equation are equal, but one may be much faster compute than the other.
Forwarded from کانال اطلاع رسانی دانشکده علوم ریاضی
#سخنرانی
#عنوان: ملاحضات فلسفی علومداده
سخنران: دکتر توسرکانی
تاریخ برگزاری: چهارشنبه 22 آذر 1396
#ساعت: 13:30
محل برگزاری: تالار اجتماعات گروه فلسفه و علم دانشگاه صنعتی شریف
🖍کانال دانشکده علوم ریاضی
@mathshariff 🇮🇷
#عنوان: ملاحضات فلسفی علومداده
سخنران: دکتر توسرکانی
تاریخ برگزاری: چهارشنبه 22 آذر 1396
#ساعت: 13:30
محل برگزاری: تالار اجتماعات گروه فلسفه و علم دانشگاه صنعتی شریف
🖍کانال دانشکده علوم ریاضی
@mathshariff 🇮🇷
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The bridges of Königsberg
Watch a short video introducing the Könisberg problem and Euler’s solution - BARABASI
Watch a short video introducing the Könisberg problem and Euler’s solution - BARABASI
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Zooming into the World Wide Web Watch an online video that zooms into the WWW sample that has lead to the discovery of the scale-free property - BARABASI
🔖 Cascading Failures as Continuous Phase-Space Transitions
Yang Yang, Adilson E. Motter
🔗 https://arxiv.org/pdf/1712.04053
📌 ABSTRACT
In network systems, a local perturbation can amplify as it propagates, potentially leading to a large-scale cascading failure. Here we derive a continuous model to advance our understanding of cascading failures in power-grid networks. The model accounts for both the failure of transmission lines and the desynchronization of power generators, and incorporates the transient dynamics between successive steps of the cascade. In this framework, we show that a cascade event is a phase-space transition from an equilibrium state with high energy to an equilibrium state with lower energy, which can be suitably described in closed form using a global Hamiltonian-like function. From this function we show that a perturbed system cannot always reach the equilibrium state predicted by quasi-steady-state cascade models, which would correspond to a reduced number of failures, and may instead undergo a larger cascade. We also show that in the presence of two or more perturbations, the outcome depends strongly on the order and timing of the individual perturbations. These results offer new insights into the current understanding of cascading dynamics, with potential implications for control interventions.
Yang Yang, Adilson E. Motter
🔗 https://arxiv.org/pdf/1712.04053
📌 ABSTRACT
In network systems, a local perturbation can amplify as it propagates, potentially leading to a large-scale cascading failure. Here we derive a continuous model to advance our understanding of cascading failures in power-grid networks. The model accounts for both the failure of transmission lines and the desynchronization of power generators, and incorporates the transient dynamics between successive steps of the cascade. In this framework, we show that a cascade event is a phase-space transition from an equilibrium state with high energy to an equilibrium state with lower energy, which can be suitably described in closed form using a global Hamiltonian-like function. From this function we show that a perturbed system cannot always reach the equilibrium state predicted by quasi-steady-state cascade models, which would correspond to a reduced number of failures, and may instead undergo a larger cascade. We also show that in the presence of two or more perturbations, the outcome depends strongly on the order and timing of the individual perturbations. These results offer new insights into the current understanding of cascading dynamics, with potential implications for control interventions.
🎩 "Sixty years of percolation"
Hugo Duminil-Copin
🔗 https://arxiv.org/abs/1712.04651
🎒 This is an introduction to percolation from a mathematical perspective, but for a broad audience of mathematicians.
Hugo Duminil-Copin
🔗 https://arxiv.org/abs/1712.04651
🎒 This is an introduction to percolation from a mathematical perspective, but for a broad audience of mathematicians.
🎞 Here's a video of Timothy Gowers' talk, gave in Tromso a few weeks ago about the state of academic publishing, and about why a system whose flaws are obvious to almost everybody is as robust as it is.
https://mediasite.uit.no/Mediasite/Play/db5614d2d8de4b528b62929b5209355d1d?PlayFrom=2400000&_utm_source=1-2-2
https://mediasite.uit.no/Mediasite/Play/db5614d2d8de4b528b62929b5209355d1d?PlayFrom=2400000&_utm_source=1-2-2